Tree Quantum Field Theory

Abstract

We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively {\it differential} renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a nonperturbative definition of field theory in noninteger dimension.

20 pages, 6 figures

References in corpus (7)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space
• Constructive ${\varphi }^4$ field theory without tears
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Constructive Matrix Theory
• Parametric Representation of Noncommutative Field Theory
• Parametric representation of "critical" noncommutative QFT models

Cited by in corpus (11)

• How to Resum Feynman Graphs
• Loop Vertex Expansion for Phi^2k Theory in Zero Dimension
• A Perspective on Constructive Quantum Field Theory
• Constructive Field Theory in Zero Dimension
• Rigorous quantum field theory functional integrals over the p-adics I: anomalous dimensions
• Complete monotonicity for inverse powers of some combinatorially defined polynomials
• The Ground State Energy of The Massless Spin-Boson Model
• Tree expansion in time-dependent perturbation theory
• Exotic R^4 and quantum field theory
• Constructive expansion for quartic vector fields theories. I. Low dimensions
• Mode d'emploi de la théorie constructive des champs bosoniques (A user's guide to bosonic constructive field theory)